Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Enstad, Ulrik"'
We give an explicit criterion for a rational lattice in the time-frequency plane to admit a Gabor frame with window in the Schwartz class. The criterion is an inequality formulated in terms of the lattice covolume, the dimension of the underlying Euc
Externí odkaz:
http://arxiv.org/abs/2408.03423
We show that any free action of a connected Lie group of polynomial growth on a finite dimensional locally compact space has finite tube dimension. This is shown to imply that the associated crossed product C*-algebra has finite nuclear dimension. As
Externí odkaz:
http://arxiv.org/abs/2307.15013
This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups are linearly independent whenever the associated twisted group ring doe
Externí odkaz:
http://arxiv.org/abs/2302.01202
Let $G$ be a second-countable amenable group with a uniform $k$-approximate lattice $\Lambda$. For a projective discrete series representation $(\pi, \mathcal{H}_{\pi})$ of $G$ of formal degree $d_{\pi} > 0$, we show that $D^-(\Lambda) \geq d_{\pi} /
Externí odkaz:
http://arxiv.org/abs/2208.05896
Autor:
Enstad, Ulrik, Raum, Sven
We introduce a notion of covolume for point sets in locally compact groups that simultaneously generalizes the covolume of a lattice and the reciprocal of the Beurling density for amenable, unimodular groups. This notion of covolume arises naturally
Externí odkaz:
http://arxiv.org/abs/2207.05125
This note provides new criteria on a unimodular group $G$ and a discrete series representation $(\pi, \mathcal{H}_{\pi})$ of formal degree $d_{\pi} > 0$ under which any lattice $\Gamma \leq G$ with $\text{vol}(G/\Gamma) d_{\pi} \leq 1$ (resp. $\text{
Externí odkaz:
http://arxiv.org/abs/2112.05502
Publikováno v:
Journal of Functional Analysis, Volume 283, Issue 6, 2022
This paper provides sufficient density conditions for the existence of smooth vectors generating a frame or Riesz sequence in the lattice orbit of a square-integrable projective representation of a nilpotent Lie group. The conditions involve the prod
Externí odkaz:
http://arxiv.org/abs/2107.13850
Autor:
Enstad, Ulrik
Publikováno v:
Journal of Mathematical Analysis and Applications Volume 511, Issue 2, 15 July 2022
We consider converses to the density theorem for irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that under the right assumpt
Externí odkaz:
http://arxiv.org/abs/2103.14467
We generalize Feichtinger and Kaiblinger's theorem on linear deformations of uniform Gabor frames to the setting of a locally compact abelian group $G$. More precisely, we show that Gabor frames over lattices in the time-frequency plane of $G$ with w
Externí odkaz:
http://arxiv.org/abs/2001.07080
Autor:
Enstad, Ulrik
Publikováno v:
J. Math. Pures Appl. (9) 139 (2020), 143--176
Let $\Lambda$ be a lattice in a second countable, locally compact abelian group $G$ with annihilator $\Lambda^{\perp} \subseteq \widehat{G}$. We investigate the validity of the following statement: For every $\eta$ in the Feichtinger algebra $S_0(G)$
Externí odkaz:
http://arxiv.org/abs/1905.06827